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Introduction to Linear Algebra (Addison-Wesley Series in Mathematics) download epub

by Serge Lang

Epub Book: 1460 kb. | Fb2 Book: 1464 kb.

Series: Addison-Wesley Series in Mathematics.

Series: Addison-Wesley Series in Mathematics. Lang covers the basics of vectors, matrices, vector spaces, and linear mappings. No background in mathematics is assumed, although the reader should probably be familiar with the sort of elementary algebra and trigonometry taught in grade school.

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Introduction to Linear Algebra. Excellent! Rigorous yet straightforward, all answers included!"―Dr. J. Adam, Old Dominion University.

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Lang's Algebra, a graduate-level introduction to abstract algebra . Lang engaged in several efforts to challenge anyone he believed was spreading misinformation or misusing science or mathematics to further their own goals.

It has affected all subsequent graduate-level algebra books. It contained ideas of his teacher, Artin; some of the most interesting passages in Algebraic Number Theory also reflect Artin's influence and ideas that might otherwise not have been published in that or any form.

A Radical Approach to Algebra (Addison-Wesley Series in Mathematics). 7 Mb. Theory of International Politics (Addison-Wesley series in political science). Grady Booch, James Rumbaugh, Ivar Jacobson.


ADDISON -WESLEY PUBLISHING COMPANY Reading, Massachusetts Menlo Park, California, London, Don Mills, Ontario. Cover photograph by courtesy of Spencer-Phillips and Green, Kentfield, California. Years ago, the colleges used to give courses in college algebra and other subjects which should have been covered in high school. More recently, such courses have been thought unnecessary, but some experiences I have had show that they are just as necessary as ever.

Start by marking Linear algebra (Addison-Wesley series in mathematics) as Want to Read . and maybe it's also my natural aversion to linear algebra. in any case i don't think it's one of lang's best books. good exercises though

Start by marking Linear algebra (Addison-Wesley series in mathematics) as Want to Read: Want to Read savin. ant to Read. good exercises though. as i recall it's sometimes lacking in examples perhaps it was the class i used this book for, but i thought this book wasn't the most well organized.

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Other readers will always be interested in your opinion of the books you've read. Whether you've loved the book or not, if you give your honest and detailed thoughts then people will find new books that are right for them. Sieve Methods, Exponential Sums, and their Applications in Number Theory.

180 page paperback book a Introduction to Linear Algebra.

Comments: (7)

I purchased this book to accompany a typical introductory linear algebra class, and have since used it for reference and review in subsequent mathematics and physics classes. Lang covers the basics of vectors, matrices, vector spaces, and linear mappings. No background in mathematics is assumed, although the reader should probably be familiar with the sort of elementary algebra and trigonometry taught in grade school. On a few occasions, applications to problems in calculus are mentioned (usually in the exercises), but these can be easily skipped by those unprepared without any loss of continuity.

The book is written in the classical style typical of university-level mathematics: the main ideas are organized into theorems, which are stated precisely and proved completely. Nevertheless, Lang also includes plenty of exposition and examples, especially in the early chapters. Most theorems and definitions are followed by a list of examples.

Chapter 1 introduces vectors as directed line segments which can be represented by n-tuples (a list of n numbers) and specify a point in n-space. Concepts like dot products, norms, and orthogonality are introduced in this setting.

Chapter 2 introduces matrices and matrix algebra. Then, the standard procedure for solving systems of linear equations using matrices is given, followed by the important interpretations involving the column vectors of the coefficient matrix. Some of the proofs in this chapter (especially in section 5 covering elementary matrices) are fairly messy--I imagine impatient readers might have some difficulty here.

Chapter 3 reintroduces vectors as elements of an abstract vector space. The approach is logical and straightforward: the chapter begins with the axioms that define a vector space, and then quickly moves on to linear combinations, linear independence, bases, and dimension. Although this all seems very sensible for someone already familiar with the material, I suspect that students new to linear algebra (especially those studying by themselves) will be taken by surprise by the abrupt generalization. After becoming comfortable with vectors as "arrows in space", suddenly, integers and matrices and functions can all be vectors, too. I think an introductory text would benefit from more careful motivation of new ideas like this.

Chapters 4 and 5 discuss linear mappings. Lang also returns to systems of linear equations, which can now be given new interpretations.

Chapter 6 covers scalar products and orthogonality for abstract vectors, including a very gentle introduction to Fourier series. The standard Gram-Schmidt algorithm for finding orthogonal bases is covered in detail.

Chapter 7 covers determinants. My only complaint about this chapter is its tardiness: determinants are very useful throughout linear algebra (for instance, when determining whether a set of vectors is linearly independent, or when discussing the orientation of a basis and orientation-preservation of a mapping) and should be introduced earlier.

Chapter 8 covers eigenvectors and eigenvalues. In section 3, Lang associates eigenvector problems with the optimization of quadratic forms over a sphere using calculus. This is an interesting geometric interpretation which is skipped in the other introductory texts I have looked at.

Each chapter is divided into several short sections, which are followed by exercises. Answers, and sometimes explanations, are included in the back of the book. I have not done many of the exercises because I have primarily used this book for reference, but those that I have done tend to be fairly straightforward. There are many simple computations and some more theoretical questions and proofs (but none that would take more than a few minutes). Students who want a serious challenge should find a supplementary source of problems.

Overall, this short text covers the fundamentals of the topic very well. The book is terse but rarely incomplete. There are a few shortcomings discussed above that might make the book a little unfriendly towards readers with no "mathematical maturity".

With the exception of several remarks about differential equations and Fourier series, the book is devoid of applications. Nevertheless, it is always concrete and direct, and I would still recommend it for students of applied mathematics, physics, and engineering, who will certainly benefit from a more theoretical understanding of the mathematics they use: science is no excuse for sloppy mathematics! Also, these students will find no shortage of applications of linear algebra in their scientific classes. On the other hand, I would suggest that students of the social sciences and business interested only in the raw applications of linear algebra look elsewhere.
This book is easy to understand, and very concise. There are a few printing errors, but I'm pleased with it. The answers are in the back of the book, but sadly no hints or detailed solutions. My professor chose to provide those as additional course materials, which I have found helpful.

Overall, a better than average math text.
Introduction to Linear Algebra

This book is an easy way of learning linear algebra, it is intended for undergraduate students. It is composed with the most important topics in linear algebra, sucha as linear equations, matrices, vector spaces, and much more. I highly recommend it, it has computational and conceptual type exercises.
good enough
This is not a review on the content but on the presentation of this ebook. It is full of formatting errors. Even worse, mathematical formulas are wrong in places due to incorrect formatting. Obviously this ebook must have been produced using an automated process with no proof reading. This is utterly unacceptable, especially considering that the ebook costs almost as much as the print version. Verdict: useless.
I started using this book as it was the assigned for a course. However, it's mid-semester, and I realized my book is missing pages! I'm pretty sure it's a binding issue....

I'm very disappointed, and it's a huge annoyance to pay for a textbook that is missing pages. I wanted to study for an upcoming an exam, but will have to borrow a friend's book in the meantime. Do not buy this book, get the hard-copy book if possible.
Serge Lang's Introduction to Linear Algebra provides a nice introduction to the subject. The text, which is designed for a one semester course for students who are taking or have completed multi-variable calculus, covers the basic theory and computational techniques. Since the emphasis is on proving theorems rather than the applications that are of interest to physical scientists, engineers, and economists, the text is best suited to pure mathematics students.

Topics are motivated, the theory is carefully developed, computational techniques are demonstrated through clearly written examples, and geometric interpretations of the algebra are discussed. The exposition is generally clear, but I occasionally had to turn to Blyth and Robertson's Basic Linear Algebra 2nd Edition or Friedberg, Insel, and Spence's Linear Algebra (4th Edition) for clarification when examples were lacking (notably in the section on eigenvalues and eigenvectors that precedes the introduction of the characteristic polynomial). Another caveat is that there are also numerous errors, including some in the answer key.

The exercises consist of computational problems, which require meticulous attention to detail, and proofs of results that extend the topics developed in the text. The exercises are organized thematically in order to teach concepts not covered in the body of the text. Some problems are reintroduced after additional material has been developed, so that you can solve them in new, more efficient, ways, thereby demonstrating the power of the new techniques that you are learning. Answers to most of the exercises are provided in an appendix, making the text suitable for self-study.

The text begins with a review of vectors. This material is drawn from Lang's Calculus of Several Variables (Undergraduate Texts in Mathematics) and should be familiar to most readers. Next, Lang demonstrates how matrix algebra can be used to solve systems of linear equations. While the reader presumably learned how to solve systems of linear equations in high school (or even earlier), the discussion of homogeneous linear equations, row operations, and linear combinations provides the foundation for subsequent topics in the book.

The remainder of the book is devoted to finite-dimensional vector spaces. Once Lang introduces the basic definitions, he covers linear independence, the basis of a vector space, and dimension. This leads to a discussion of linear mappings, their representation by matrices, and how the kernel and image of these maps are related to the rank of the matrix of linear transformation. Lang discusses composition of mappings and inverse mappings before delving into scalar products, orthogonal bases, and bilinear maps. Lang then develops the theory of determinants and discusses how to apply them to solving systems of linear equations, finding the inverse of a matrix, and calculating areas and volumes. After introducing eigenvectors, eigenvalues, and the characteristic polynomial, Lang concludes the book with a discussion of the eigenvectors and eigenvalues of symmetric matrices that uses the earlier material on scalar products and orthogonality.

Much of this material is drawn from Lang's Linear Algebra (Undergraduate Texts in Mathematics), where it is treated in more depth. However, that text is written for students already familiar with basic matrix manipulations, so it does not discuss elementary matrices or Gaussian elimination. Understanding it also requires greater mathematical sophistication.

This text is limited in scope. If you are preparing to do graduate work in mathematics, you will need to read an additional text such as Lang's Linear Algebra, Friedberg, Insel, and Spence's Linear Algebra, Hoffman and Kunze's Linear Algebra (2nd Edition), Axler's Linear Algebra Done Right, or Blyth and Robertson's Further Linear Algebra. Of these, the one that is most suitable for self-study is Further Linear Algebra.

If you are interested in an introductory text that is suitable for self-study, you may wish to consider Blyth and Robertson's Basic Linear Algebra as an alternative to this one, as it includes abundant examples and answers to almost all the exercises.
Introduction to Linear Algebra (Addison-Wesley Series in Mathematics) download epub
Author: Serge Lang
ISBN: 0201042061
Category: Science & Math
Subcategory: Mathematics
Language: English
Publisher: Springer Verlag; 1st edition (June 1, 1970)
Pages: 176 pages